Question

if b is between A and C and AB=3X, BC=6X+1, and AC=19. find x and BC

Answer 1

Let's draw the situation.

Based on the sum of segments property, we can define the following equation.

$AC=AB+BC$

Replacing the given expressions, we have

$19=3x+6x+1$

Let's solve for x

$\begin{gathered} 19-1=9x \\ 9x=18 \\ x=\frac{18}{9} \\ x=2 \end{gathered}$

We use this value to find BC.

$BC=6x+1=6(2)+1=12+1=13$

Therefore, segment BC is 13 units long.